No abstract

In this paper a general derivation is given of equations describing the variance of an arbitrary detector response in a Monte Carlo simulation and the average number of collisions a particle will suffer until its history ends. The theory is validated for a simple slab system using the two-direction transport model and for a two-group infinite system, which both allow analytical solutions. Numerical results from the analytical solutions are compared with actual Monte Carlo calculations, showing excellent agreement. These analytical solutions demonstrate the possibilities for optimizing the weight window settings with respect to variance. Using the average number of collisions as a measure for the simulation time a cost function inversely proportional to the usual Figure of Merit is defined, which allows optimization with respect to overall efficiency of the Monte Carlo calculation. For practical applications it is outlined how the equations for the variance and average number of collisions can be solved using a suitable existing deterministic neutron transport code with adapted number of energy groups and scattering matrices.